A fast Galerkin-based method for eigenfrequencies in acoustics of small rooms with slanted boundary planes

This paper proposes a Galerkin-type numerical algorithm for an efficient calculation of low eigenfrequencies for rectangular parallelepiped rooms with slanted boundary planes, in the frequency interval (0,200)Hz, with the volume V≤200m3. The main idea of the algorithm is to apply a system of Galerkin׳s basis functions which are orthogonal, after a certain change of variables, in a unit cube. As a result, the problem is reduced to a classical problem of the computational algebra about eigenvalues of a symmetric matrix. If applied to any parallelepiped of non-splayed geometry, the algorithm automatically gives the known classical modes. For rooms with the splayed planes, the sought mode frequencies can precisely be calculated in real time on a personal computer, by taking from 11 to 13 basis functions along each coordinate axis. Some particular examples are considered, in order to demonstrate the capability of the proposed algorithm, as well as its precision with a change of basis functions. It is also seen from the discussed examples that splaying the boundary planes can indeed make more uniform distribution of the low natural frequencies.